Rate-Theory Model of Polymer Crystallization

Abstract

A new lattice model of polymer crystallization is described. Results of numerical solutions of rate equations for crystallization of a two-dimensional "crystal" are presented. It is shown that the crystal thickness varies inversely with supercooling and that kinetics similar to secondary nucleation occurs. This is true even though the growth face is intrinsically rough and hence there cannot be any nucleation. The presence of a low-entropy saddle point during growth is explained, and its influence on the crystal thickness and lamellar morphology is discussed.PACS numbers: 61.50.Cj, 61.41, +e, 82.60,Nh Crystals of long-chain molecules invariably grow as lamellae that are usually much thinner than the length of the chains. '2 Molecules traverse the lamellae many times; the geometry is described in detail below. The precise manner of this folding has been the subject of considerable debate, but the emphasis of this paper is instead the origin of the lamellar habit. This phenomenon has been explained by models that invoke secondary nucleation; i.e. , the nucleation of new layers of the crystal on the advancing edge of the lamella. 3 5The kinetics is also consistent with this mechanism, 5 7 yet the crystals do not always have the faceted edges required for the nucleation process. 's In those cases where crystals of a polymer can be grown with either straight or smoothly rounded morphologies, the latter tend to occur at higher temperatures. It has been proposed that this change is associated with surface roughening. 9'o At the higher temperatures the surface is intrinsically rough on a microscopic scale, since steps across the growth faces and other favorable growth sites are generated by thermal fluctuations in equilibrium. Nucleation of a new layer is not required under these conditions. For growth faces of infinite extent, the theory of the roughening transition is now well established, "' and experimental verification has been obtained. " We now develop further a model of polymer crystallization that applies to rough growth faces and which could also be relevant when the faces are straight. The model reproduces the principal trends in experimental measurements of lamellar thickness and growth rates. The growth face can only be sufficiently rough if the stems (the straight sequences of chain which traverse the crystal) are allowed to vary in length and if short stems are allowed. Our model considers the basic unit of crystallization to be a short sequence of chain (e.g. , six CH2 units of polyethylene; cf. Refs. 4 and 9 and Point'6); stems differ in length according to how many units they contain.The geometry of the crystals is described schematically in Fig. 1(a) with each stem corresponding to a prism. The ends of the stems should be imagined as having attached chains emerging from the crystalline region. In many cases (e.g. , to the left of the diagram) the chains will be folded back into the lamella. Partly attached chains with loops are indicated at the growth surface. Effects of polymer chain connectivity and ...

Intramolecular Nucleation Model for Polymer Crystallization

“…5,6 At higher temperatures, the growth front may be rough and growth is limited by the entropic cost to form a sufficiently flat surface by thermal fluctuationssthis is the situation considered by the Sadler-Gilmer model. [7][8][9] Although there exist several theoretical models for the mechanism of polymer crystallization, the role of molecular weight in polymer crystallization is still poorly understood. For instance, we have no satisfactory explanation for the phenomenon of polymer-size segregation during crystal growth.…”

Kinetic Monte Carlo simulations of the growth of polymer crystals

“…The second approach, which was developed by Sadler and Gilmer and has been termed the entropic barrier model, is based upon the interpretation of kinetic Monte Carlo simulations 8,9 and rate-theory calculations [10][11][12] of a simplified model of polymer crystal growth. As with the surface nucleation approach, the observed thickness is suggested to result from the competition between a driving force and a free energy barrier contribution to the growth rate.…”

A Review on Polymer Crystallization Theories

“…In 1983, Sadler and Gilmer [105] took this idea to extremes and argued that the nucleation barrier is completely an "entropy barrier" without enthalpic contribution. Meanwhile, they proposed that the regime transition from I to II corresponded to the transition from rough surface nucleation to smooth surface nucleation [85,105,106].…”